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CN-121995958-A - Self-adjusting preset performance consistency control method for multi-agent system

CN121995958ACN 121995958 ACN121995958 ACN 121995958ACN-121995958-A

Abstract

The invention discloses a self-adjusting preset performance consistency control method of a multi-agent system, which comprises the steps of establishing a mathematical model of the multi-agent system, defining synchronous errors of follower agents, describing information interaction relations among agents in the multi-agent system based on graph theory, defining performance constraint and self-adjusting performance boundary functions of the synchronous errors, introducing a boundary adjustment mechanism with safety interval detection to dynamically adapt to disturbance, mapping the synchronous errors constrained by the preset performance boundary into unconstrained variables through error conversion and barrier functions, designing virtual controllers of various steps, a final actual controller and self-adaption rate based on a back-stepping method, and realizing collaborative tracking control of the multi-agent system. The invention can solve the problems of feasibility of initial conditions, rigid constraint of fixed performance boundary and limitation of symmetrical performance, can cope with burst interference through a self-adjusting mechanism while ensuring overshoot, convergence time and steady-state precision, and remarkably improves the robustness of the system.

Inventors

  • Qiu Baiqi
  • LIU ZHI

Assignees

  • 广东工业大学
  • 人工智能与数字经济广东省实验室(广州)

Dates

Publication Date
20260508
Application Date
20260209

Claims (9)

  1. 1. A method for self-regulating predetermined performance consistency control of a multi-agent system, comprising: establishing a mathematical model of a multi-agent system comprising a follower agent and a leader agent, and defining a synchronization error of the follower agent; Describing information interaction relations among the intelligent agents in the multi-intelligent agent system based on graph theory; defining performance constraint and self-adjusting performance boundary functions of the synchronous errors, and introducing a boundary adjustment mechanism with safety interval detection to dynamically adapt to disturbance; Mapping the synchronous error constrained by the preset performance boundary into an unconstrained variable through error conversion and an obstacle function, so that a constraint control problem is converted into a stability control problem for the unconstrained variable; based on the back-stepping method, each-order virtual controller, a final actual controller and the self-adaptive rate are recursively designed to ensure that all signals of a closed-loop system are bounded and realize the collaborative tracking control of a multi-agent system.
  2. 2. The method for self-regulating predetermined performance uniformity control for a multi-agent system according to claim 1, wherein the first step is The kinetic model of the individual follower agent is: (1); Wherein, the , The total number of follower agents; And Is a vector of the state of the system, Representing a system state; represents the first Total order of individual follower agents; Representing a system control input; represents the first The output of the individual follower agents; And Is an unknown smooth nonlinear function; And Represents a bounded external disturbance, meets , Wherein And Is an unknown constant; the dynamics of the leader agent are: (2); Wherein, the An output signal representing the leader agent, The output signal of the leader agent and its derivative are known, smooth and bounded.
  3. 3. The method for self-tuning predetermined performance consistency control of a multi-agent system according to claim 2, wherein the follower agent is not capable of obtaining global information but only local information, considering the actual situation, defining Is the first Neighbor set of individual follower agent, define the first The synchronization error of the individual follower agents is: (3); Wherein, the Is the first Neighbor number received by individual follower agent The information weight of the individual agent(s), Is the first The information weight of the leader agent is received by the individual follower agents.
  4. 4. A method of self-regulating predetermined performance consistency control of a multi-agent system according to claim 3, wherein describing information interaction relationships between agents in the multi-agent system based on graph theory comprises: networked communication through directed graph for multi-agent system Representing a directed graph Comprising node sets Edge set for defining legal communication channels And adjacency matrix for quantizing link weights When the agent is From the intelligent body In the course of the receipt of the information, At this time, the agent Is an intelligent body Excluding self-connections, i.e. The input degree of each intelligent agent is represented by an input degree matrix Representation of wherein The dynamic process of information propagation is encoded in a Laplace matrix In, at the same time define As a communication weight matrix Time-representative agent Information of the leader can be received, and it is assumed that Thereby ensuring that at least one follower agent can acquire the information of the leader agent, and the expansion chart is recorded as Wherein , , ; Expansion map There is one spanning tree, where the leader node is its root node; Is a non-singular matrix , And The following inequality describes the synchronization error Error from actual tracking Relationship between: (4); in the formula, Representing the minimum eigenvalue of the matrix.
  5. 5. The self-regulating, predetermined performance consistency control method of a multi-agent system of claim 4, wherein defining the performance constraint for synchronization errors and the self-regulating performance boundary function comprises: the performance constraint of the synchronization error is defined as follows: (5); Wherein, the And The expression of (2) is: (6); the self-adjusting performance boundary function includes the following components: 1) Inverse tuning function And initial value of synchronization error 2) Performance scalar functions And 3) Boundary adjusting function And 。
  6. 6. The method for self-regulating predetermined performance uniformity control of a multi-agent system according to claim 5, wherein the inverse tuning function For subsequent error conversion, defined as: (7); Wherein, the Represents convergence time; For adjustable design parameters, which are determined The larger the value of the convergence speed, the faster the convergence; The method meets the following conditions: At least second order continuous micro-functional and ; When (when) Tends to be In the time-course of which the first and second contact surfaces, And for the following , ; Performance scalar function Acting as a reference function of the reference, The method is used for ensuring the critical transient and steady-state performances of the system, and is defined as follows: (8); In the time-course of which the first and second contact surfaces, From the slave Monotonically decrease to And at Is kept as Parameter(s) Control of The larger the value of the convergence speed, the faster the convergence; Boundary adjusting function The expression of (2) is: (9); Wherein the method comprises the steps of Designing parameters; Is the self-adaptive rate; And Is a dynamic adjustment factor, which is generated by the following auxiliary systems: (10); (11); Here the number of the elements to be processed is, , , Is designed as a parameter and is set at the time of initialization , ; Representing a symbolic function And A detection function preset inside the performance boundary is defined as: (12)。
  7. 7. The method of claim 6, wherein the operating logic of the boundary adjustment function is: Boundary detection when synchronization error Is positioned in a preset safety interval, namely, meets When driving item So that the regulating factor And Kept at zero and further boundary adjustment function At this point, the performance boundary need not be modified, wherein, And Determining the size of a safety zone; Out of range response if Beyond the safety interval, corresponding drive item To adjust the factor And Dynamically increasing to drive the boundary adjusting function by equation (9) And Changes occur, a relaxation of the performance boundaries is achieved, wherein, And Determining boundary adjusting force; Boundary restoration when After returning to the safety interval, the regulating factor And Will be at the parameters of And The dominant exponential rate converges to zero, restoring the performance boundary to the original setting.
  8. 8. The method of self-regulating predetermined performance uniformity control for a multi-agent system according to claim 6, wherein said synchronization error is transformed by a tuning function defined by equation (7) to meet a feasible initial condition requirement, an introduced error variable The initial value is zero, defined as follows: (13); under this transformation, the performance constraint defined by equation (5) is equivalently transformed into the following form: (14); Wherein a new boundary function And Is defined as follows: (15) If the expression (14) is established, the system is ensured to have the following performances: the initial conditions are naturally met due to And Push out Naturally stands; transient performance is bounded over time intervals In, by Export out By adjusting parameters And The method realizes the reservation of transient indexes such as overshoot; Steady state accuracy assurance when When the system meets When (1) There is Ensuring the steady-state accuracy of the synchronization error; To achieve the performance constraint described by equation (14), the constrained error variable Mapping as unconstrained variables The transformation relationship is as follows: (16)。
  9. 9. the method for self-regulating predetermined performance uniformity control of a multi-agent system according to claim 8, wherein a back-step control method is employed to construct virtual controllers of each order , Actual controller Adaptive rate 、 Comprising: defining error variables : (17); Wherein, the The first order filter is output, and the expression of the first order filter is as follows: (18); in the formula, In order to design the parameters of the device, The virtual controller is to be designed; according to the recursive flow of the back-stepping method, a virtual controller is designed The following are provided: (19); in the formula, 、 、 In order to design the parameters of the device, And For adaptation rate, intermediate variables And The definition is as follows: (20); (21); Design of actual controller Adaptive rate 、 The following are provided: (22); (23); in the formula, 、 For design parameters, intermediate variables And The definition is as follows: (24); (25); in the formula, 、 Is a design parameter.

Description

Self-adjusting preset performance consistency control method for multi-agent system Technical Field The invention relates to the technical field of multi-agent system control, in particular to a self-adjusting preset performance consistency control method of a multi-agent system. Background The Multi-agent system (Multi-AGENT SYSTEMS, MAS) has wide application prospect in various key fields such as intelligent power grid dispatching, unmanned aerial vehicle formation control, satellite constellation coordination, distributed sensor network and the like by virtue of the core advantages of high cost benefit, strong expandability, good fault tolerance capability and the like. In these application scenarios, consistency control is one of the basic and core technologies of implementing collaborative operations by a multi-agent system, and aims to synchronize and coordinate states or outputs of multiple agents. In recent years, based on the recursive design framework of the back-stepping method, various control schemes have been proposed in the industry to solve the problem of consistent control of multi-agent systems. However, in many practical engineering systems, fast and accurate reference tracking is a key premise for ensuring safe and reliable operation of the system. For this reason, related art has developed high performance control methods such as predetermined performance control (Prescribed Performance Control, PPC), funneling control (Funnel Control), etc., which allow designers to quantitatively predefine transient and steady state performance indicators of synchronization errors, including critical parameters such as convergence time, overshoot, steady state accuracy, etc. The prior art has the following main defects: First, initial condition feasibility problems. Most existing high performance control methods have strict requirements on the feasible initial conditions, i.e. the initial value of the synchronization error must be within the performance envelope. This means that when the system is restarted, the reference value is suddenly changed or suffers from external disturbance, it is necessary to additionally check whether the initial condition is satisfied, and if not, the performance function is selected again, which significantly increases the complexity of the design and implementation of the controller. The existing solutions mainly adopt tuning functions to adjust errors or construct symmetric performance functions with initial values of infinity, but the former cannot clearly preset performance boundaries (such as overshoot) in transient stages, and the latter easily cause poor transient behaviors (such as overlarge error peaks). Second, the rigid constraint problem of the fixed performance boundary. Existing predetermined performance control methods typically choose a pair of fixed, monotonically varying functions over time to construct a performance boundary, predefining the desired transient and steady state responses. However, in some practical application scenarios, sudden factors such as sudden interference (e.g., large-amplitude interference), severe fluctuation of the reference value, etc. may cause significant increase of errors, even touch or break through performance boundaries, and finally cause control failure. Typical examples are unmanned aircraft upwind flight scenarios, where the flight controller needs to achieve a dynamic balance between control performance and the capabilities of the aircraft itself to ensure safe and stable flight. Third, limitations of symmetric performance constraints. In an actual engineering system, performance constraint of error regulation often presents significant asymmetric characteristics, namely constraint indexes such as a deviation tolerance, a convergence rate and the like allowed by errors in positive and negative fluctuation are often different. The traditional symmetrical performance constraint scheme is difficult to adapt to the actual demands, and the problems of control precision reduction, stability weakening or energy consumption increase and the like are easily caused. Therefore, the development of the preset performance control method with self-regulating capability and capable of simultaneously processing the feasibility of initial conditions, the adaptability to sudden disturbance and the asymmetric performance constraint has important practical significance and application value for improving the reliability of the multi-agent system consistency control. Disclosure of Invention The invention aims to overcome the defects of the prior art and provide a self-adjusting preset performance consistency control method of a multi-agent system, which can not only ensure that the dynamic process and steady-state performance (including overshoot, convergence time and steady-state precision) of a synchronous error can be preset as required and automatically meet initial conditions, but also can elastically relax performance boundaries w